Without any code, it's hard to say. What are you making the call with? Does your simple request/response node app work as a cli module or how did you do it? Can you call the other rest API from node REPL?
The problem could be in your code, or it could be that some of the libraries you required that overwrote or changed functionalities you use.
If you have that working simple req/res node app, can you make it a module? Super simple module - just export a "run" function, and then call that module/function from your main app - just to see what's going on. If this works from, say, cli, but not from your app, it's most likely that your main app changes some functionality that you use.